Aircraft: WIDEBODY; LOW WING; 4 TURBOJET ENG
Phase of flight: Cruise
Anomaly: ATC Issue All Types; Airspace Violation All Types; Conflict Airborne Conflict; Deviation / Discrepancy - Procedural Published Material / Policy

While working Sector XX/XY combined. Traffic volume was low; I had plenty of time to listen and hear what was happening around the room and to pre-plan my next few steps based on URET information. I knew there was an AR200 flight of two coming to my sector and was preparing for any odd military requests based on this. I heard an adjacent Controller (Sector XZ) take a request from the Aircraft X; to initiate a flight break up. Aircraft X forwarded the requested break up to the adjacent Controller. The adjacent Controller took the information and then proceeded to switch the aircraft to my frequency after acceptance of the handoff. I then queried the other Controller at Sector XZ; 'Do you have anything you need to tell me about Aircraft X?' The adjacent Controller said; 'I'm a little busy; I have three things going on.' Which is possible but still no excuse to not forward coordination information to me. The flight asks for a break up. Aircraft X and Aircraft Y request a split and I proceed to tag up Aircraft Y. I radar identify Aircraft Y and clear the aircraft on course to its requested route; a radial off of ZZZ ([a] VOR). I had traffic for Aircraft Y so I could only initially offer a vector away from the Aircraft X to allow Aircraft Y to climb from FL240 back to the Aircraft Y's orbit of FL350. During the middle of this I also had to vector out Aircraft X away from a ZZZ1 arrival [Aircraft Z] in order to get the [ZZZ1 arrival] down to meet its crossing restriction of FL270. This is a situation that should never arise. The unwritten rule in the area is AR200 shall not have arrivals stacked on top of the refueling track simply because there is little room to get the aircraft down. Back to Aircraft Y; as I continue to re-evaluate the Aircraft Y's flight I realize I cannot clear the aircraft higher than FL300 due to crossing FL310 traffic and I cannot clear Aircraft Y back to the orbit because there is a limited data block descending through my airspace without a handoff or point out. I asked the adjacent Controller (Sector XZ) what is this limited and he failed to acknowledge my question. I then proceeded to hand off Aircraft Y to Sector XZ on a heading to avoid the intruder limited. The adjacent Controller at Sector XZ was frustrated that Aircraft Y was left on a heading and without control turns the aircraft 90 degrees to the left and climbs the aircraft to FL350 in my airspace on course towards the requested ZZZ radial to resume the orbit. I then asked the Sector XZ Controller; what is going on with the Aircraft Y; he says; 'I'm not working him. [Another area] must have turned the airplane'. In all; the adjacent Controller fed me a no win situation of a ZZZ1 arrival on top of a flight breakup and violated my airspace twice.I know that [this reporting tool] is not a snitch program. I also understand as a reporting tool cadre that the intent of the program is to learn from situations. However I fear that the freedom from punishment or training has made many controllers lackadaisical in their duties and responsibilities. I do not understand how one individual can routinely violate the regulations without some form of correction. I explained the situation to my Supervisor and was told there isn't much she can do simply because she must build a case against the individual. I know the QA/QC order defines what kind of corrections can be taken and steps for this to occur. My real question is; 'What am I supposed to do as a controller?' I am witnessing negligence and am put into situations that I cannot; by law; look the other way on. I know people turn aircraft in each others airspace. I know not all appreq's are completed. I also know I don't want to be a snitch or complainer. I know this isn't the correct avenue to handle this problem. But what recourse do I have? The 7110 says that If I see an unsafe situation that I must do my best to correct it. 7110.65; 2-1-16; 'Do notassume that because someone else has responsibility for the aircraft that the unsafe situation has been observed and the safety alert issued; inform the appropriate controller.' Hence this report. I am more than happy to entertain any questions you may have. Please feel free to contact me. Controller reports of complacent Controller at the next sector who isn't pointing out aircraft or following facility SOP; which leads reporter to become frustrated about the other controllers work ethics.